ATLANTA — As the Republican contenders turn in earnest to the Super Tuesday states, Mitt Romney’s next challenge is to convert a slender Michigan win into something bigger: an unshakable lead in the presidential contest.

Rick Santorum’s runner-up primary finishes Tuesday there and in Arizona left the party establishment breathing easier, though there seemed little optimism that a nomination fight that has sapped the resources of GOP donors and weakened their likely nominee’s standing with independent voters would end anytime soon.

“Romney is a fragile front-runner, but there is much less panic in Republican ranks than there was 24 hours ago,” said Washington lobbyist Ed Rogers, a White House political adviser in the Ronald Reagan and George H.W. Bush administrations. “The notion of Santorum at the top of the ticket frightened a lot of people. That chance has been reduced, but it hasn’t been extinguished.”

Rogers, a donor to several GOP presidential candidates, including Romney, said that if the former Massachusetts governor does extremely well in the 10-state Super Tuesday contests next week, “you’ll start to hear people of stature call for an end to this.” But even Romney advisers regard that as unlikely. Instead, it could take months before any contender can put a mathematical lock on the 1,144 delegates needed to win the nomination.

On Wednesday, Romney locked in on economic issues — promising a small crowd at a rainy rally in Toledo, Ohio, that he would crack down much harder on China for unfair trade practices than President Barack Obama has. He avoided mention of his GOP rivals.

Santorum, meantime, was in Tennessee, another Tuesday primary state. Behind the scenes, his campaign was pushing for resolution of the delegate count in Michigan. The final tally is expected to show a near-even split with Romney — the state allocates delegates largely by congressional district — and Santorum tried to claim a belated moral victory despite his 3-percentage-point loss in the overall vote.

Michigan “was a huge win for us,” Santorum told reporters after speaking to a crowd of about 1,000 at Temple Baptist Church in Powell, Tenn., near Knoxville, many of them conservatively dressed students from nearby Crown College. “We are out here today heading to Super Tuesday with some wind at our back.”

Next Tuesday, Republican voters will award the biggest delegate haul so far this year — more than 400 in all. Super Tuesday, however, is considerably less super than past versions, as fewer states hold contests on that day and new party rules spread the delegates more proportionately among the GOP contenders. As a result, the eight primaries and three caucuses are unlikely to generate a decisive overall victory for anyone.

The owners of Boulder’s Sterling University Peaks apartments, who this summer were cited for illegally subdividing 92 bedrooms in the complex, have reached an agreement to settle the case for $410,000, the city announced Thursday.